Fractional Control of a Single-Link Flexible Manipulator

2005 ◽  
Author(s):  
Vicente Feliu ◽  
Blas M. Vinagre ◽  
Concepcio´n A. Monje
Keyword(s):  
Low Frequency ◽  
Nonlinear Effects ◽  
Flexible Manipulator ◽  
Phase System ◽  
Low Frequency Vibration ◽  
Control Scheme ◽  
Single Link ◽  
The Time Domain ◽  
Tip Mass ◽  
Fractional Controller

A new method to control single-link lightweight flexible manipulators in the presence of changes in the load is proposed in this paper. The overall control scheme consists of three nested control loops. Once the friction and other nonlinear effects have been compensated, the inner loop is designed to give a fast motor response. The middle loop decouples the dynamics of the system, and reduces its transfer function to a double integrator. A fractional-derivative controller is used to shape the outer loop into the form of a fractional-order integrator. The result is a constant-phase system with, in the time domain, step responses exhibiting constant overshoot, independently of variations in the load. Continuous and discrete approximate implementations of the fractional controller are simulated. Comparison of the responses to a step command of the manipulator controlled with the proposed approximations and with the ideal fractional controller showed that the latter could be accurately approximated by standard continuous and discrete controllers of high order preserving the robustness. An interesting feature of this control scheme is that the overshoot is independent of the tip mass. This allows a constant safety zone to be delimited for any given placement task of the arm, independently of the load being carried, thereby making it easier to plan collision avoidance. Simulations also include comparison with standard PD controller, and verification of the assumption of dominant low-frequency vibration mode.

scholarly journals A Reduced-Order Model for Active Suppression Control of Vehicle Longitudinal Low-Frequency Vibration

2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Donghao Hao ◽  
Changlu Zhao ◽  
Ying Huang
Keyword(s):  
Longitudinal Vibration ◽  
Estimation Method ◽  
Low Frequency ◽  
Coupling Model ◽  
Torsional Stiffness ◽  
Model Parameters ◽  
Active Suppression ◽  
Low Frequency Vibration ◽  
Time Domain Response ◽  
The Time Domain

Establishing a prediction model, with linearity and few dof (degree of freedom), is a key step for the design of a control algorithm based on the modern control theory. In this paper, such a model is needed for active suppression of vehicle longitudinal low-frequency vibration. However, many dynamic processes in the vehicle have different effects on the vibration. Therefore, a detailed coupling model is firstly established, considering the dynamics of the torsional vibrations of the driveline and the tire, the tire force nonlinearity, and the vehicle vertical and pitch vibrations. Based on this model, sensitivity analysis is conducted and the results show that the tire slip, the torsional stiffness of the half-shaft, and the tire have great influences on the longitudinal vibration. Then a three-dof model is obtained by linearizing the tire slip into damping. A parameter estimation method is designed to obtain the model parameters. Finally, the model is validated. The time domain response, error analysis, and frequency response results demonstrate that the 3-dof model has a good consistency with the detailed coupling model. It is suitable as a control-oriented model.

A force observation method for tracking control of flexible-link manipulators

Robotica ◽  
2012 ◽  
Vol 31 (4) ◽  
pp. 669-677 ◽  
Author(s):  
S. Farokh Atashzar ◽  
M. Shahbazi ◽  
H. A. Talebi ◽  
F. Towhidkhah
Keyword(s):  
Tracking Control ◽  
Flexible Manipulator ◽  
Control Technique ◽  
Flexible Link ◽  
Robust Controller ◽  
Estimation Errors ◽  
Control Scheme ◽  
Lyapunov Redesign ◽  
Single Link ◽  
Observation Method

SUMMARYIn this paper, a composite controller is proposed for single-link flexible manipulators exposed to external tip force disturbances. In the proposed scheme, the extended Kalman filter is utilized to observe the environmental forces and the Lyapunov redesign robust controller is applied to control the destabilizing effect of the observation errors in noisy situations. The observed force can be utilized in different applications (such as tele-surgical robotics) in order to eliminate the necessity of additional force sensors. This fact is important for structural miniaturization and cost reduction. The main contributions of this paper are (1) proposing a disturbance observation technique for in-contact flexible link manipulators (note that the challenge of Jacobian singularity is studied as a possible diverging factor of the observation) and (2) proposing the composite robust controller to eliminate the destabilizing effect of estimation errors. The advantages of the proposed control scheme over the conventional techniques are analyzed. Simulation results are given for a single-link flexible manipulator to illustrate the effectiveness of the composite control technique and experimental results are given to validate the performance of the observation method.

Piezoelectric generator with nonlinear structure

2021 ◽  
pp. 146442072110086
Author(s):  
Liming Zhou ◽  
Yanbo Liu ◽  
Long Ma ◽  
Yue Wu
Keyword(s):  
Resonance Frequency ◽  
Low Frequency ◽  
Electrical Energy ◽  
Bending Vibration ◽  
Low Frequency Vibration ◽  
Piezoelectric Cantilever ◽  
Piezoelectric Generator ◽  
Ritz Procedure ◽  
Tip Mass ◽  
Euler Bernoulli Beam

Motion in nature is usually a low-frequency vibration such as walking, running, swinging arms, and so on, but traditional piezoelectric cantilever structures are inefficient at harvesting energy from low-frequency vibrations. T in the environment. To overcome this, a novel piezoelectric generator was designed. A cantilevered bimorph with a tip mass and a pair of preloading springs were fixed on its base to form a nonlinear piezoelectric generator. The energy transmission in the structure was analyzed. The harvester was modeled as a Euler–Bernoulli beam, and the piezoelectric material was assumed to be linear. The bending vibration was calculated using the Rayleigh–Ritz procedure, and the frequency characteristics of the output voltage were analyzed under different preloading distances. It was found that changing the preloading of the spring helped reduce the natural frequency of the cantilever, which facilitated conversion of ambient low-frequency vibrations into electrical energy. Then, the characteristics of low frequency energy harvesting were investigated experimentally. The theoretical results were consistent with the experimental data; moreover, the resonance frequency, which changes with the preloading distance, reduced from 43 to 35 Hz when the preloading distance was increased from 0 to 1 mm. In this paper, an effective structure to control the resonant frequency is proposed and its motion equation stated. The structure has potential for applications in predicting the effect of preloading distance on resonance frequency.

scholarly journals Optimized output-based input shaping for control of single-link flexible manipulator using linear matrix inequality

2020 ◽  
Vol 20 (1) ◽  
pp. 109
Author(s):  
Nura Musa Tahir ◽  
Mustapha Muhammad ◽  
Bashir Bala Muhammad ◽  
Haliru Liman ◽  
Aminu Yahaya Zimit ◽  
...  
Keyword(s):  
Linear Matrix Inequality ◽  
Hybrid Control ◽  
Flexible Manipulator ◽  
Linear Matrix ◽  
Response Analysis ◽  
Matrix Inequality ◽  
Loop Control ◽  
Control Scheme ◽  
Single Link ◽  
Hybrid Control Scheme

<span>Precise hub angle positioning due to tip deflections, flexible motions and under various payloads is enormous tasks in the control of single-link flexible manipulators. In this paper, output-based command shaping (OBCS) was designed using the system output for tip deflections and residuals vibrations suppression, and this was incorporated with a linear matrix inequality (LMI) closed-loop control scheme for precise hub angle positioning.  The robustness of the hybrid control scheme was tested by changing the payloads from 0g to 30g, and 50g. Simulation results showed that endpoint residuals vibrations and tip deflections due to flexible motions were suppressed and hence precise hub angle positioning under various payloads was achieved. Integral absolute error (IAE), Integral square error (ISE) and Time response analysis (TRA) were used as the performance indexes. Hence, the hybrid control scheme is simple and robust.</span>

Non Linear System Identification of Offshore Floating Structures

2008 ◽  
Author(s):  
Nadathur P. Varadarajan ◽  
Satish Nagarajaiah
Keyword(s):  
Frequency Response ◽  
Hilbert Transform ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Nonlinear Effects ◽  
Floating Structure ◽  
Floating Structures ◽  
Spar Platforms ◽  
The Time Domain ◽  
Non Linear System

Floating structures such as spar platforms are typically designed to be compliant or move with environment loadings, rather than resisting them. Hence they are designed so that there is no dynamic amplification in wave frequency response. However, higher order nonlinear effects are produced in low frequency wind excited regions, especially in Spar platforms. It is difficult to separate the nonlinear behavior of the model response from the loading using conventional methods. In this paper, Empirical Mode Decomposition and Hilbert Transform (EMD/HT) is used to identify the nonlinear response of a spar from the model test results. From the measured response the dynamic parameters are estimated as follows: 1) The multi-component response of the floating structure is decomposed into IMF components. 2) Hilbert transform of the input and the IMF signal in the time domain is done to extract the instantaneous dynamic characteristics. 3) Amplitude and frequency dependent frequency response function is used to represent the result of HT identification. The EMD method can identify any changes in system properties in real time and can be effectively used for repair and retrofit.

Vibration Modeling of Arc-Based Cantilevers for Energy Harvesting Applications

2014 ◽  
Vol 1 (1-2) ◽  
Author(s):  
Daniel J. Apo ◽  
Mohan Sanghadasa ◽  
Shashank Priya
Keyword(s):  
Energy Harvesting ◽  
Low Frequency ◽  
Substrate Thickness ◽  
Cantilever Beams ◽  
Vibration Energy Harvesting ◽  
Low Frequency Vibration ◽  
Vibration Model ◽  
Bending Mode ◽  
Out Of Plane ◽  
Tip Mass

AbstractCantilever beams are widely used for designing transducers for low-frequency vibration energy harvesting. However, in order to keep the dimensions within reasonable constraints, a large tip mass is generally required for reducing the resonance frequency below 100 Hz which has adverse effect on the reliability. This study provides a breakthrough toward realizing low-frequency micro-scale transduction structures. An analytical out-of-plane vibration model for standalone arc-based cantilever beams was developed that includes provisions for shear and rotary inertia, multidirectional arcs, and multiple layers. The model was applied to a multilayered cantilever beam (10-mm wide and 0.1-mm thick) composed of three arcs, and the results indicate that the fundamental bending mode of the beam was 38 Hz for a silicon substrate thickness of 100 μm. The model was validated with modal experimental results from an arc-based cantilever made out of aluminum.

scholarly journals Modeling and simulation for low-frequency vibration energy harvesting based on piezoelectric unimorph cantilever beam

2018 ◽  
Vol 208 ◽  
pp. 04003
Author(s):  
Binjie Song ◽  
Jianhai Yue ◽  
Zhunqing Hu
Keyword(s):  
Energy Harvester ◽  
Low Frequency ◽  
Mathematic Model ◽  
Vibration Energy Harvesting ◽  
Modal Frequency ◽  
First Order ◽  
Low Frequency Vibration ◽  
Generating Capacity ◽  
Piezoelectric Unimorph ◽  
Tip Mass

In order to solve the problem of sustainable energy supply for low-power electronic products used in low-frequency vibration environment, the mathematic model was established based on the theory of piezoelectricity and Euler-Bernoulli beam. Also, the effects of different parameters of PZT unimorph beams such as the length, width, and tip mass on generating capacity were studied by FEM. The results show that the energy harvester with PZT unimorph beam and tip mass is suitable for low-frequency vibration environment. Increasing the length or reducing the width of the beam can significantly lower the first-order modal frequency of energy harvester when other conditions remain the same. Within certain range, the first-order modal frequency of the beam also gradually reduced as the tip mass increasing. When the size of the PZT unimorph beam is 60x60x0.33mm, the tip mass is 8.92g and an exciting force of 0.01N is applied to it along z axis, an output of 8.1V can be obtained. Meanwhile, the PZT unimorph beam is under the first vibration mode and the resonant frequency is 16.296Hz.

scholarly journals Vibration Control of Manipulators with Flexible Nonprismatic Links Using Piezoelectric Actuators and Sensors

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Valdecir Bottega ◽  
Alexandre Molter ◽  
Jun S. O. Fonseca ◽  
Rejane Pergher
Keyword(s):  
Tracking Control ◽  
Low Frequency ◽  
Piezoelectric Actuators ◽  
Lyapunov Stability Theory ◽  
Control Model ◽  
Torque Control ◽  
Flexible Manipulator ◽  
Lagrange Equations ◽  
Low Frequency Vibration ◽  
Piezoelectric Actuators And Sensors

This work presents a tracking control model for a flexible nonprismatic link robotic manipulator using simultaneously motor torques and piezoelectric actuators. The dynamic model of the flexible manipulator is obtained in a closed form through the Lagrange equations. The control uses the motor torques for the joints tracking control and also to reduce the low-frequency vibration induced in the manipulator links. The stability of this control is guaranteed by the Lyapunov stability theory. Piezoelectric actuators and sensors are added for controlling vibrations with frequencies beyond the reach of motor torque control. The naturals frequencies are calculated by the finite element method, and the approximated eigenfunctions are interpolated by polynomials. Three eigenfunctions are used for the dynamics of the arm, while only two are used for the control. Numerical experiments on Matlab/Simulink are used to verify the efficiency of the control model.

Fault diagnosis in yaw drive induction motor for wind turbine

2018 ◽  
Vol 42 (6) ◽  
pp. 576-595 ◽  
Author(s):  
Ali Ouanas ◽  
Ammar Medoued ◽  
Mourad Mordjaoui ◽  
Abdesselam Lebaroud ◽  
Djamel Sayad
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Low Frequency ◽  
Offshore Wind ◽  
Discrete Wavelet ◽  
Phase System ◽  
Offshore Wind Turbines ◽  
Three Phase ◽  
The Time Domain ◽  
The Hilbert Transform

Wind turbines are widely exploited throughout the world. The availability and reliability of offshore wind turbines are asking to impose a constant maintenance strategy. In this work, we propose a method that allows filtering the signal of the frequency inverter that feeds the yaw drive used in wind turbine. The redundant information is eliminated via discrete wavelet transform and empirical modal decomposition. The two types of faults are detected from the envelope of the Hilbert transform. The magnitude imbalance detection is carried out in the time domain. The root mean square values of the envelopes of the three-phase system have a good indicator for the fuzzy system to evaluate the severity of the defect. In the frequency domain, the signature of the broken bar fault is located in the low-frequency bandwidth. The harmonics appeared in the spectrum sensitive in amplitude and frequency to the variation of load. Experimental results have demonstrated the accuracy of the proposed method.

Optimized FOPID Control of a Single Link Flexible Manipulator (SLFM) Using Genetic Algorithm

2014 ◽  
Vol 704 ◽  
pp. 336-340 ◽  
Author(s):  
Ahmed Bensenouci ◽  
Mohamed Shehata
Keyword(s):  
Genetic Algorithm ◽  
Cost Function ◽  
Objective Function ◽  
Flexible Manipulator ◽  
System Response ◽  
Basic Model ◽  
Optimum Parameters ◽  
Control Scheme ◽  
Single Link ◽  
Fractional Order Pid

This paper implements Fractional Order PID (FOPID) controller to control the rotate angle of a Single Link Flexible Manipulator (SLFM). The optimum parameters were found using Genetic Algorithm where a cost function based on the Integral Sqarred Error, ISE, index (cost/objective function) was minimized. The basic model is presented and the operating principle of the device is discussed. A control scheme to increase the system damping and improve the system response is proposed where a FOPID controller is used. To show the effectiveness of the designed controller, its responses, following divers tests, were compared to those obtained using an optimized PID with GA and using the same cost function. The results show encouragement to pursue further this research axis.

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